4x^2+16x-28=0

Simple and best practice solution for 4x^2+16x-28=0 equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

Solution for 4x^2+16x-28=0 equation: 


Simplifying
4x2 + 16x + -28 = 0

Reorder the terms:
-28 + 16x + 4x2 = 0

Solving
-28 + 16x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-7 + 4x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-7 + 4x + x2)' equal to zero and attempt to solve:

Simplifying
-7 + 4x + x2 = 0

Solving
-7 + 4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + 4x + 7 + x2 = 0 + 7

Reorder the terms:
-7 + 7 + 4x + x2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 4x + x2 = 0 + 7
4x + x2 = 0 + 7

Combine like terms: 0 + 7 = 7
4x + x2 = 7

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 7 + 4

Reorder the terms:
4 + 4x + x2 = 7 + 4

Combine like terms: 7 + 4 = 11
4 + 4x + x2 = 11

Factor a perfect square on the left side:
(x + 2)(x + 2) = 11

Calculate the square root of the right side: 3.31662479

Break this problem into two subproblems by setting 
(x + 2) equal to 3.31662479 and -3.31662479.


Subproblem 1
x + 2 = 3.31662479

Simplifying
x + 2 = 3.31662479

Reorder the terms:
2 + x = 3.31662479

Solving
2 + x = 3.31662479

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + x = 3.31662479 + -2

Combine like terms: 2 + -2 = 0
0 + x = 3.31662479 + -2
x = 3.31662479 + -2

Combine like terms: 3.31662479 + -2 = 1.31662479
x = 1.31662479

Simplifying
x = 1.31662479


Subproblem 2
x + 2 = -3.31662479

Simplifying
x + 2 = -3.31662479

Reorder the terms:
2 + x = -3.31662479

Solving
2 + x = -3.31662479

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + x = -3.31662479 + -2

Combine like terms: 2 + -2 = 0
0 + x = -3.31662479 + -2
x = -3.31662479 + -2

Combine like terms: -3.31662479 + -2 = -5.31662479
x = -5.31662479

Simplifying
x = -5.31662479


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.31662479, -5.31662479}
Solution
x = {1.31662479, -5.31662479}

See similar equations:

| -x^2+7-10=0 | | 3+d3–d | | -3x=23 | | 113-2x=16x+17 | | -(1+7k)-8k=7-7k | | 125d+12=3500 | | 9t^3-64t=0 | | (2x-3)2= | | 2(4a-12)+3a=6a | | 3r+7=16 | | 4/3=x | | 8X=13Y | | -3(x+2)-1=2(x-5)-5x | | 12-10x=102-45x | | 3+(4*8)56= | | 3x-1=32 | | 4c-3=25 | | x+(1.5x)=45000 | | 49=-6c+9+2c | | 8(2n-2)=2(8n-8) | | 3y^2-5y+8=0 | | .50*-3= | | 3y^2-5y=8 | | 3/4(4x-8)=2/3(6x+15) | | 4(x+2)/4=26 | | -8(x+6)+4=-44 | | 4c-3=35 | | 3(x-5)/2=18 | | x+4=3x-5 | | 7m-8m+2=3 | | 8(4u--1)-12u=11(2u-6) | | 2(x+4)=5(3x-7)-3(x+2) |

Equations solver categories